Question

tell whether the ratios form a proportion.

1. \\(\frac{4}{7}, \frac{24}{35}\\)
2. \\(\frac{8}{24}, \frac{5}{15}\\)

Explanation:

Problem 16: $\boldsymbol{\frac{4}{7},\frac{24}{35}}$

Step1: Cross - multiply the ratios

To check if two ratios $\frac{a}{b}$ and $\frac{c}{d}$ form a proportion, we use the cross - multiplication property. That is, we check if $a\times d=b\times c$.
For the ratios $\frac{4}{7}$ and $\frac{24}{35}$, we have $a = 4$, $b = 7$, $c = 24$, and $d = 35$.
So, $a\times d=4\times35 = 140$ and $b\times c=7\times24=168$.

Step2: Compare the cross - products

Since $140
eq168$, the two ratios do not form a proportion.

Problem 17: $\boldsymbol{\frac{8}{24},\frac{5}{15}}$

Step1: Simplify the ratios (optional, but can help)

First, simplify $\frac{8}{24}$. We can divide both the numerator and the denominator by their greatest common divisor, which is 8. So, $\frac{8\div8}{24\div8}=\frac{1}{3}$.
Next, simplify $\frac{5}{15}$. The greatest common divisor of 5 and 15 is 5. So, $\frac{5\div5}{15\div5}=\frac{1}{3}$.

Step2: Check if the simplified ratios are equal

Since both ratios simplify to $\frac{1}{3}$, the ratios $\frac{8}{24}$ and $\frac{5}{15}$ form a proportion. We can also use cross - multiplication: $8\times15 = 120$ and $24\times5=120$. Since $8\times15 = 24\times5$, the ratios form a proportion.

Answer:

s:

1. The ratios $\frac{4}{7}$ and $\frac{24}{35}$ do not form a proportion.
2. The ratios $\frac{8}{24}$ and $\frac{5}{15}$ form a proportion.